Imaginary numbers are more important than they might appear on the surface; with
ID: 3115916 • Letter: I
Question
Imaginary numbers are more important than they might appear on the surface; without them, you can’t solve quadratic equations or figure out inequalities. So, in this class—and in any setting in which you work with quadratic equations—you’ll need to know how to use imaginary numbers. For instance, as you see in Section 6.2 of Algebra for College Students, imaginary numbers apply to equations for right triangles.
When might you need to find the side of a right triangle? Describe a real-life situation in which you might need to rely on this skill, and provide an equation you could use to solve it.
Explanation / Answer
When might you need to find the side of a right triangle?
Let's say Rocky told you a story, "I want to go from point A to B via your car. But you can't go directly to B, you will have to travel x km to reach to C and then take a right turn and travel (x-4) km to reach to B. Calculate x if the direct distance between A to B is 2km." Is he lying or narrating the truth?
x^2+(x-4)^2 = 2^2
2x^2 -4x + 16 = 4
x^2 -2x + 6 = 0
D = b^2 - 4ac = -20 < 0
so this is an imaginary triangle and doesn't have real information.
so Rocky is lying.